Prove the following.tan4θ + tan2θ = sec4θ - sec2θ

Taking LHStan4θ + tan2θ= tan2θ( tan2θ + 1)= (sec2θ - 1)(sec2θ) [1 + tan2θ = sec2θ]= sec4θ - sec2θ= RHSProved !

Q5 of 45 Page 138

Prove the following.
tan⁴θ + tan²θ = sec⁴θ - sec²θ

Taking LHS

tan⁴θ + tan²θ

= tan²θ( tan²θ + 1)

= (sec²θ - 1)(sec²θ) [1 + tan²θ = sec²θ]

= sec⁴θ - sec²θ

= RHS

Proved !

Prove the following.

sec²θ + cosec²θ = sec²θ × cosec²θ

Prove the following.

cot²θ - tan²θ = cosec²θ - sec²θ

Prove the following.

sec⁶x – tan⁶x = 1 + 3 sec²x × tan²x

Questions · 45

6. Trigonometry

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